where \( d(t) \) is detector data. Â
2. Sensitivity Estimate
  - For \( h_0 \sim 10^{-24} \) (predicted amplitude), LIGO O4 can detect SNR > 5 with 1 yr integration. Â
Validation
- Null Test: Inject synthetic signals into noise to verify recovery. Â
- Frequency Binning: Search for excess power in 32--38 Hz bins (Fig. 5a). Â
CMB Spiral-Phase Correlations
Prediction
Spiral harmonics \( \psi_{nlm} \propto e^{im\phi + \beta \ln r} \) imprint helical phase patterns in CMB polarization: Â
\[B_\ell^m \sim \int \psi_{nlm} \cdot \nabla T \, d\Omega,\] Â
where \( T \) is the temperature anisotropy. These generate: Â